Here are some common (and less common) parent functions:
name
\(f(x)=\)
constant
1
linear
\(x\)
absolute
\(|x|\)
quadratic
\(x^2\)
cubic
\(x^3\)
reciprocal
\(\frac{1}{x}\)
square root
\(\sqrt{x}\)
cube root
\(\sqrt[3]{x}\)
sine
\(\sin(x)\)
cosine
\(\cos(x)\)
tangent
\(\tan(x)\)
ceiling
\(\lceil x \rceil\)
floor
\(\lfloor x \rfloor\)
exponential
\(e^x\)
logarithmic
\(\ln(x)\)
logistic
\(\frac{e^x}{e^x+1}\)
squared reciprocal
\(\frac{1}{x^2}\)
Match the graphs with their names.
Solution
You could try graphing the options or referencing a parent-function chart.
Question
Here are some common (and less common) parent functions:
name
\(f(x)=\)
constant
1
linear
\(x\)
absolute
\(|x|\)
quadratic
\(x^2\)
cubic
\(x^3\)
reciprocal
\(\frac{1}{x}\)
square root
\(\sqrt{x}\)
cube root
\(\sqrt[3]{x}\)
sine
\(\sin(x)\)
cosine
\(\cos(x)\)
tangent
\(\tan(x)\)
ceiling
\(\lceil x \rceil\)
floor
\(\lfloor x \rfloor\)
exponential
\(e^x\)
logarithmic
\(\ln(x)\)
logistic
\(\frac{e^x}{e^x+1}\)
squared reciprocal
\(\frac{1}{x^2}\)
Match the graphs with their names.
Solution
You could try graphing the options or referencing a parent-function chart.
Question
Here are some common (and less common) parent functions:
name
\(f(x)=\)
constant
1
linear
\(x\)
absolute
\(|x|\)
quadratic
\(x^2\)
cubic
\(x^3\)
reciprocal
\(\frac{1}{x}\)
square root
\(\sqrt{x}\)
cube root
\(\sqrt[3]{x}\)
sine
\(\sin(x)\)
cosine
\(\cos(x)\)
tangent
\(\tan(x)\)
ceiling
\(\lceil x \rceil\)
floor
\(\lfloor x \rfloor\)
exponential
\(e^x\)
logarithmic
\(\ln(x)\)
logistic
\(\frac{e^x}{e^x+1}\)
squared reciprocal
\(\frac{1}{x^2}\)
Match the graphs with their names.
Solution
You could try graphing the options or referencing a parent-function chart.
Question
Here are some common (and less common) parent functions:
name
\(f(x)=\)
constant
1
linear
\(x\)
absolute
\(|x|\)
quadratic
\(x^2\)
cubic
\(x^3\)
reciprocal
\(\frac{1}{x}\)
square root
\(\sqrt{x}\)
cube root
\(\sqrt[3]{x}\)
sine
\(\sin(x)\)
cosine
\(\cos(x)\)
tangent
\(\tan(x)\)
ceiling
\(\lceil x \rceil\)
floor
\(\lfloor x \rfloor\)
exponential
\(e^x\)
logarithmic
\(\ln(x)\)
logistic
\(\frac{e^x}{e^x+1}\)
squared reciprocal
\(\frac{1}{x^2}\)
Match the graphs with their names.
Solution
You could try graphing the options or referencing a parent-function chart.
Question
Here are some common (and less common) parent functions:
name
\(f(x)=\)
constant
1
linear
\(x\)
absolute
\(|x|\)
quadratic
\(x^2\)
cubic
\(x^3\)
reciprocal
\(\frac{1}{x}\)
square root
\(\sqrt{x}\)
cube root
\(\sqrt[3]{x}\)
sine
\(\sin(x)\)
cosine
\(\cos(x)\)
tangent
\(\tan(x)\)
ceiling
\(\lceil x \rceil\)
floor
\(\lfloor x \rfloor\)
exponential
\(e^x\)
logarithmic
\(\ln(x)\)
logistic
\(\frac{e^x}{e^x+1}\)
squared reciprocal
\(\frac{1}{x^2}\)
Match the graphs with their names.
Solution
You could try graphing the options or referencing a parent-function chart.
Question
Here are some common (and less common) parent functions:
name
\(f(x)=\)
constant
1
linear
\(x\)
absolute
\(|x|\)
quadratic
\(x^2\)
cubic
\(x^3\)
reciprocal
\(\frac{1}{x}\)
square root
\(\sqrt{x}\)
cube root
\(\sqrt[3]{x}\)
sine
\(\sin(x)\)
cosine
\(\cos(x)\)
tangent
\(\tan(x)\)
ceiling
\(\lceil x \rceil\)
floor
\(\lfloor x \rfloor\)
exponential
\(e^x\)
logarithmic
\(\ln(x)\)
logistic
\(\frac{e^x}{e^x+1}\)
squared reciprocal
\(\frac{1}{x^2}\)
Match the graphs with their names.
Solution
You could try graphing the options or referencing a parent-function chart.
Question
Here are some common (and less common) parent functions:
name
\(f(x)=\)
constant
1
linear
\(x\)
absolute
\(|x|\)
quadratic
\(x^2\)
cubic
\(x^3\)
reciprocal
\(\frac{1}{x}\)
square root
\(\sqrt{x}\)
cube root
\(\sqrt[3]{x}\)
sine
\(\sin(x)\)
cosine
\(\cos(x)\)
tangent
\(\tan(x)\)
ceiling
\(\lceil x \rceil\)
floor
\(\lfloor x \rfloor\)
exponential
\(e^x\)
logarithmic
\(\ln(x)\)
logistic
\(\frac{e^x}{e^x+1}\)
squared reciprocal
\(\frac{1}{x^2}\)
Match the graphs with their names.
Solution
You could try graphing the options or referencing a parent-function chart.
Question
Here are some common (and less common) parent functions:
name
\(f(x)=\)
constant
1
linear
\(x\)
absolute
\(|x|\)
quadratic
\(x^2\)
cubic
\(x^3\)
reciprocal
\(\frac{1}{x}\)
square root
\(\sqrt{x}\)
cube root
\(\sqrt[3]{x}\)
sine
\(\sin(x)\)
cosine
\(\cos(x)\)
tangent
\(\tan(x)\)
ceiling
\(\lceil x \rceil\)
floor
\(\lfloor x \rfloor\)
exponential
\(e^x\)
logarithmic
\(\ln(x)\)
logistic
\(\frac{e^x}{e^x+1}\)
squared reciprocal
\(\frac{1}{x^2}\)
Match the graphs with their names.
Solution
You could try graphing the options or referencing a parent-function chart.
Question
Here are some common (and less common) parent functions:
name
\(f(x)=\)
constant
1
linear
\(x\)
absolute
\(|x|\)
quadratic
\(x^2\)
cubic
\(x^3\)
reciprocal
\(\frac{1}{x}\)
square root
\(\sqrt{x}\)
cube root
\(\sqrt[3]{x}\)
sine
\(\sin(x)\)
cosine
\(\cos(x)\)
tangent
\(\tan(x)\)
ceiling
\(\lceil x \rceil\)
floor
\(\lfloor x \rfloor\)
exponential
\(e^x\)
logarithmic
\(\ln(x)\)
logistic
\(\frac{e^x}{e^x+1}\)
squared reciprocal
\(\frac{1}{x^2}\)
Match the graphs with their names.
Solution
You could try graphing the options or referencing a parent-function chart.
Question
Here are some common (and less common) parent functions:
name
\(f(x)=\)
constant
1
linear
\(x\)
absolute
\(|x|\)
quadratic
\(x^2\)
cubic
\(x^3\)
reciprocal
\(\frac{1}{x}\)
square root
\(\sqrt{x}\)
cube root
\(\sqrt[3]{x}\)
sine
\(\sin(x)\)
cosine
\(\cos(x)\)
tangent
\(\tan(x)\)
ceiling
\(\lceil x \rceil\)
floor
\(\lfloor x \rfloor\)
exponential
\(e^x\)
logarithmic
\(\ln(x)\)
logistic
\(\frac{e^x}{e^x+1}\)
squared reciprocal
\(\frac{1}{x^2}\)
Match the graphs with their names.
Solution
You could try graphing the options or referencing a parent-function chart.
Question
Consider the quadratic function graphed below:
What is the interval(s) over which the function is positive?
What is the interval(s) over which the function is negative?
What is the interval(s) over which the function is increasing?
What is the interval(s) over which the function is decreasing?
What is the domain (in interval notation)?
What is the range (in interval notation)?
Solution
Positive: (-7,1)
Negative: (-inf,-7)U(1,inf)
Increasing: (-inf,-3)
Decreasing: (-3,inf)
Domain: (-inf,inf)
Range: (-inf,7]
Question
Consider the quadratic function graphed below:
What is the interval(s) over which the function is positive?
What is the interval(s) over which the function is negative?
What is the interval(s) over which the function is increasing?
What is the interval(s) over which the function is decreasing?
What is the domain (in interval notation)?
What is the range (in interval notation)?
Solution
Positive: (-inf,-8)U(0,inf)
Negative: (-8,0)
Increasing: (-4,inf)
Decreasing: (-inf,-4)
Domain: (-inf,inf)
Range: [-1,inf)
Question
Consider the quadratic function graphed below:
What is the interval(s) over which the function is positive?
What is the interval(s) over which the function is negative?
What is the interval(s) over which the function is increasing?
What is the interval(s) over which the function is decreasing?
What is the domain (in interval notation)?
What is the range (in interval notation)?
Solution
Positive: (-inf,-3)U(5,inf)
Negative: (-3,5)
Increasing: (1,inf)
Decreasing: (-inf,1)
Domain: (-inf,inf)
Range: [-2,inf)
Question
Consider the quadratic function graphed below:
What is the interval(s) over which the function is positive?
What is the interval(s) over which the function is negative?
What is the interval(s) over which the function is increasing?
What is the interval(s) over which the function is decreasing?
What is the domain (in interval notation)?
What is the range (in interval notation)?
Solution
Positive: (-5,3)
Negative: (-inf,-5)U(3,inf)
Increasing: (-inf,-1)
Decreasing: (-1,inf)
Domain: (-inf,inf)
Range: (-inf,4]
Question
Consider the quadratic function graphed below:
What is the interval(s) over which the function is positive?
What is the interval(s) over which the function is negative?
What is the interval(s) over which the function is increasing?
What is the interval(s) over which the function is decreasing?
What is the domain (in interval notation)?
What is the range (in interval notation)?
Solution
Positive: (-6,-2)
Negative: (-inf,-6)U(-2,inf)
Increasing: (-inf,-4)
Decreasing: (-4,inf)
Domain: (-inf,inf)
Range: (-inf,5]
Question
Consider the quadratic function graphed below:
What is the interval(s) over which the function is positive?
What is the interval(s) over which the function is negative?
What is the interval(s) over which the function is increasing?
What is the interval(s) over which the function is decreasing?
What is the domain (in interval notation)?
What is the range (in interval notation)?
Solution
Positive: (-inf,-7)U(3,inf)
Negative: (-7,3)
Increasing: (-2,inf)
Decreasing: (-inf,-2)
Domain: (-inf,inf)
Range: [-5,inf)
Question
Consider the quadratic function graphed below:
What is the interval(s) over which the function is positive?
What is the interval(s) over which the function is negative?
What is the interval(s) over which the function is increasing?
What is the interval(s) over which the function is decreasing?
What is the domain (in interval notation)?
What is the range (in interval notation)?
Solution
Positive: (-inf,-2)U(8,inf)
Negative: (-2,8)
Increasing: (3,inf)
Decreasing: (-inf,3)
Domain: (-inf,inf)
Range: [-6,inf)
Question
Consider the quadratic function graphed below:
What is the interval(s) over which the function is positive?
What is the interval(s) over which the function is negative?
What is the interval(s) over which the function is increasing?
What is the interval(s) over which the function is decreasing?
What is the domain (in interval notation)?
What is the range (in interval notation)?
Solution
Positive: (-5,5)
Negative: (-inf,-5)U(5,inf)
Increasing: (-inf,0)
Decreasing: (0,inf)
Domain: (-inf,inf)
Range: (-inf,7]
Question
Consider the quadratic function graphed below:
What is the interval(s) over which the function is positive?
What is the interval(s) over which the function is negative?
What is the interval(s) over which the function is increasing?
What is the interval(s) over which the function is decreasing?
What is the domain (in interval notation)?
What is the range (in interval notation)?
Solution
Positive: (-inf,0)U(6,inf)
Negative: (0,6)
Increasing: (3,inf)
Decreasing: (-inf,3)
Domain: (-inf,inf)
Range: [-1,inf)
Question
Consider the quadratic function graphed below:
What is the interval(s) over which the function is positive?
What is the interval(s) over which the function is negative?
What is the interval(s) over which the function is increasing?
What is the interval(s) over which the function is decreasing?
What is the domain (in interval notation)?
What is the range (in interval notation)?
Solution
Positive: (-5,3)
Negative: (-inf,-5)U(3,inf)
Increasing: (-inf,-1)
Decreasing: (-1,inf)
Domain: (-inf,inf)
Range: (-inf,7]
Question
Which plot matches the function:
\[f(x) = \left|{x - 1}\right| + 6\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(f(x)=|x|\), which has a vertex at the origin.
The general parameterization is \(f(x)=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=1\) and \(k=6\).
To get the correct daughter graph, translate the parent 1 units right and 6 units up. Since \(a>0\), the daughter points up.
The correct plot is Plot 4.
\[f(x) = \left|{x - 1}\right| + 6\]
Question
Which plot matches the function:
\[f(x) = \left|{x + 4}\right| - 6\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(f(x)=|x|\), which has a vertex at the origin.
The general parameterization is \(f(x)=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=-4\) and \(k=-6\).
To get the correct daughter graph, translate the parent 4 units left and 6 units down. Since \(a>0\), the daughter points up.
The correct plot is Plot 2.
\[f(x) = \left|{x + 4}\right| - 6\]
Question
Which plot matches the function:
\[f(x) = \left|{x + 2}\right| + 1\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(f(x)=|x|\), which has a vertex at the origin.
The general parameterization is \(f(x)=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=-2\) and \(k=1\).
To get the correct daughter graph, translate the parent 2 units left and 1 units up. Since \(a>0\), the daughter points up.
The correct plot is Plot 4.
\[f(x) = \left|{x + 2}\right| + 1\]
Question
Which plot matches the function:
\[f(x) = - \left|{x - 3}\right| - 6\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(f(x)=|x|\), which has a vertex at the origin.
The general parameterization is \(f(x)=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=3\) and \(k=-6\).
To get the correct daughter graph, translate the parent 3 units right and 6 units down. Since \(a<0\), the daughter points down.
The correct plot is Plot 3.
\[f(x) = - \left|{x - 3}\right| - 6\]
Question
Which plot matches the function:
\[f(x) = 4 - \left|{x + 5}\right|\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(f(x)=|x|\), which has a vertex at the origin.
The general parameterization is \(f(x)=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=-5\) and \(k=4\).
To get the correct daughter graph, translate the parent 5 units left and 4 units up. Since \(a<0\), the daughter points down.
The correct plot is Plot 3.
\[f(x) = 4 - \left|{x + 5}\right|\]
Question
Which plot matches the function:
\[f(x) = \left|{x + 4}\right| + 5\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(f(x)=|x|\), which has a vertex at the origin.
The general parameterization is \(f(x)=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=-4\) and \(k=5\).
To get the correct daughter graph, translate the parent 4 units left and 5 units up. Since \(a>0\), the daughter points up.
The correct plot is Plot 4.
\[f(x) = \left|{x + 4}\right| + 5\]
Question
Which plot matches the function:
\[f(x) = \left|{x - 3}\right| - 4\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(f(x)=|x|\), which has a vertex at the origin.
The general parameterization is \(f(x)=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=3\) and \(k=-4\).
To get the correct daughter graph, translate the parent 3 units right and 4 units down. Since \(a>0\), the daughter points up.
The correct plot is Plot 4.
\[f(x) = \left|{x - 3}\right| - 4\]
Question
Which plot matches the function:
\[f(x) = - \left|{x + 6}\right| - 4\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(f(x)=|x|\), which has a vertex at the origin.
The general parameterization is \(f(x)=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=-6\) and \(k=-4\).
To get the correct daughter graph, translate the parent 6 units left and 4 units down. Since \(a<0\), the daughter points down.
The correct plot is Plot 2.
\[f(x) = - \left|{x + 6}\right| - 4\]
Question
Which plot matches the function:
\[f(x) = 5 - \left|{x - 2}\right|\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(f(x)=|x|\), which has a vertex at the origin.
The general parameterization is \(f(x)=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=-1\) and \(h=2\) and \(k=5\).
To get the correct daughter graph, translate the parent 2 units right and 5 units up. Since \(a<0\), the daughter points down.
The correct plot is Plot 2.
\[f(x) = 5 - \left|{x - 2}\right|\]
Question
Which plot matches the function:
\[f(x) = \left|{x - 3}\right| + 1\]
Plot 1
Plot 2
Plot 3
Plot 4
Solution
The parent function is \(f(x)=|x|\), which has a vertex at the origin.
The general parameterization is \(f(x)=a\left|x-h\right|+k\). The vertex shifts to \((h,k)\). The multiplicative factor, \(a\), causes a vertical stretch and/or a vertical flip.
In this example, \(a=1\) and \(h=3\) and \(k=1\).
To get the correct daughter graph, translate the parent 3 units right and 1 units up. Since \(a>0\), the daughter points up.
The correct plot is Plot 2.
\[f(x) = \left|{x - 3}\right| + 1\]
Question
Let functions \(f\) and \(g\) be defined by the table below.
\(x\)
\(f(x)\)
\(g(x)\)
1
9
1
2
3
2
3
7
3
4
6
6
5
10
10
6
5
9
7
4
7
8
2
4
9
8
5
10
1
8
Evaluate the following:
\(f(g(3)) =\)
\(g(f(10)) =\)
\(f(f(2)) =\)
\(g(g(10)) =\)
\(f(g(g(4))) =\)
Solution
\(f(g(3))=f(3)=7\)
\(g(f(10))=g(1)=1\)
\(f(f(2))=f(3)=7\)
\(g(g(10))=g(8)=4\)
\(f(g(g(4)))=f(g(6))=f(9)=8\)
Question
Let functions \(f\) and \(g\) be defined by the table below.
\(x\)
\(f(x)\)
\(g(x)\)
1
9
9
2
7
7
3
1
3
4
6
1
5
4
2
6
3
10
7
10
4
8
5
8
9
2
6
10
8
5
Evaluate the following:
\(f(g(5)) =\)
\(g(f(10)) =\)
\(f(f(1)) =\)
\(g(g(9)) =\)
\(f(g(g(10))) =\)
Solution
\(f(g(5))=f(2)=7\)
\(g(f(10))=g(8)=8\)
\(f(f(1))=f(9)=2\)
\(g(g(9))=g(6)=10\)
\(f(g(g(10)))=f(g(5))=f(2)=7\)
Question
Let functions \(f\) and \(g\) be defined by the table below.
\(x\)
\(f(x)\)
\(g(x)\)
1
1
5
2
6
4
3
10
2
4
3
7
5
8
9
6
4
1
7
7
10
8
5
6
9
9
3
10
2
8
Evaluate the following:
\(f(g(3)) =\)
\(g(f(2)) =\)
\(f(f(10)) =\)
\(g(g(1)) =\)
\(f(g(g(8))) =\)
Solution
\(f(g(3))=f(2)=6\)
\(g(f(2))=g(6)=1\)
\(f(f(10))=f(2)=6\)
\(g(g(1))=g(5)=9\)
\(f(g(g(8)))=f(g(6))=f(1)=1\)
Question
Let functions \(f\) and \(g\) be defined by the table below.
\(x\)
\(f(x)\)
\(g(x)\)
1
4
10
2
5
7
3
9
3
4
6
9
5
8
6
6
10
1
7
3
8
8
1
2
9
2
4
10
7
5
Evaluate the following:
\(f(g(9)) =\)
\(g(f(1)) =\)
\(f(f(6)) =\)
\(g(g(7)) =\)
\(f(g(g(3))) =\)
Solution
\(f(g(9))=f(4)=6\)
\(g(f(1))=g(4)=9\)
\(f(f(6))=f(10)=7\)
\(g(g(7))=g(8)=2\)
\(f(g(g(3)))=f(g(3))=f(3)=9\)
Question
Let functions \(f\) and \(g\) be defined by the table below.
\(x\)
\(f(x)\)
\(g(x)\)
1
10
1
2
6
8
3
1
4
4
3
6
5
5
2
6
2
9
7
9
3
8
4
10
9
8
5
10
7
7
Evaluate the following:
\(f(g(3)) =\)
\(g(f(3)) =\)
\(f(f(8)) =\)
\(g(g(5)) =\)
\(f(g(g(7))) =\)
Solution
\(f(g(3))=f(4)=3\)
\(g(f(3))=g(1)=1\)
\(f(f(8))=f(4)=3\)
\(g(g(5))=g(2)=8\)
\(f(g(g(7)))=f(g(3))=f(4)=3\)
Question
Let functions \(f\) and \(g\) be defined by the table below.
\(x\)
\(f(x)\)
\(g(x)\)
1
3
8
2
5
10
3
2
6
4
7
3
5
10
5
6
9
7
7
1
2
8
8
9
9
4
4
10
6
1
Evaluate the following:
\(f(g(4)) =\)
\(g(f(5)) =\)
\(f(f(5)) =\)
\(g(g(10)) =\)
\(f(g(g(10))) =\)
Solution
\(f(g(4))=f(3)=2\)
\(g(f(5))=g(10)=1\)
\(f(f(5))=f(10)=6\)
\(g(g(10))=g(1)=8\)
\(f(g(g(10)))=f(g(1))=f(8)=8\)
Question
Let functions \(f\) and \(g\) be defined by the table below.
\(x\)
\(f(x)\)
\(g(x)\)
1
1
5
2
5
1
3
6
3
4
8
10
5
2
6
6
7
2
7
10
7
8
4
9
9
9
4
10
3
8
Evaluate the following:
\(f(g(3)) =\)
\(g(f(3)) =\)
\(f(f(8)) =\)
\(g(g(9)) =\)
\(f(g(g(7))) =\)
Solution
\(f(g(3))=f(3)=6\)
\(g(f(3))=g(6)=2\)
\(f(f(8))=f(4)=8\)
\(g(g(9))=g(4)=10\)
\(f(g(g(7)))=f(g(7))=f(7)=10\)
Question
Let functions \(f\) and \(g\) be defined by the table below.
\(x\)
\(f(x)\)
\(g(x)\)
1
6
7
2
10
1
3
8
6
4
2
10
5
5
4
6
1
8
7
7
3
8
3
5
9
4
2
10
9
9
Evaluate the following:
\(f(g(3)) =\)
\(g(f(4)) =\)
\(f(f(7)) =\)
\(g(g(8)) =\)
\(f(g(g(8))) =\)
Solution
\(f(g(3))=f(6)=1\)
\(g(f(4))=g(2)=1\)
\(f(f(7))=f(7)=7\)
\(g(g(8))=g(5)=4\)
\(f(g(g(8)))=f(g(5))=f(4)=2\)
Question
Let functions \(f\) and \(g\) be defined by the table below.
\(x\)
\(f(x)\)
\(g(x)\)
1
3
8
2
9
4
3
8
2
4
10
7
5
5
1
6
2
10
7
7
3
8
1
9
9
4
5
10
6
6
Evaluate the following:
\(f(g(3)) =\)
\(g(f(4)) =\)
\(f(f(6)) =\)
\(g(g(10)) =\)
\(f(g(g(2))) =\)
Solution
\(f(g(3))=f(2)=9\)
\(g(f(4))=g(10)=6\)
\(f(f(6))=f(2)=9\)
\(g(g(10))=g(6)=10\)
\(f(g(g(2)))=f(g(4))=f(7)=7\)
Question
Let functions \(f\) and \(g\) be defined by the table below.
\(x\)
\(f(x)\)
\(g(x)\)
1
8
5
2
1
10
3
5
8
4
7
2
5
3
1
6
6
4
7
9
7
8
10
3
9
4
9
10
2
6
Evaluate the following:
\(f(g(2)) =\)
\(g(f(7)) =\)
\(f(f(2)) =\)
\(g(g(3)) =\)
\(f(g(g(4))) =\)
Solution
\(f(g(2))=f(10)=2\)
\(g(f(7))=g(9)=9\)
\(f(f(2))=f(1)=8\)
\(g(g(3))=g(8)=3\)
\(f(g(g(4)))=f(g(2))=f(10)=2\)
Question
Let functions \(f\) and \(g\) be defined by the graph below.
Evaluate the following:
\(g(f(1)) =\)
\(f(g(8)) =\)
Solution
\(g(f(1))=g(9)=7\)
\(f(g(8))=f(9)=3\)
Question
Let functions \(f\) and \(g\) be defined by the graph below.
Evaluate the following:
\(g(f(9)) =\)
\(f(g(1)) =\)
Solution
\(g(f(9))=g(8)=3\)
\(f(g(1))=f(7)=5\)
Question
Let functions \(f\) and \(g\) be defined by the graph below.
Evaluate the following:
\(g(f(1)) =\)
\(f(g(2)) =\)
Solution
\(g(f(1))=g(6)=7\)
\(f(g(2))=f(9)=8\)
Question
Let functions \(f\) and \(g\) be defined by the graph below.
Evaluate the following:
\(g(f(1)) =\)
\(f(g(4)) =\)
Solution
\(g(f(1))=g(2)=9\)
\(f(g(4))=f(5)=5\)
Question
Let functions \(f\) and \(g\) be defined by the graph below.
Evaluate the following:
\(g(f(1)) =\)
\(f(g(1)) =\)
Solution
\(g(f(1))=g(2)=5\)
\(f(g(1))=f(7)=8\)
Question
Let functions \(f\) and \(g\) be defined by the graph below.
Evaluate the following:
\(g(f(8)) =\)
\(f(g(9)) =\)
Solution
\(g(f(8))=g(4)=6\)
\(f(g(9))=f(1)=7\)
Question
Let functions \(f\) and \(g\) be defined by the graph below.
Evaluate the following:
\(g(f(1)) =\)
\(f(g(2)) =\)
Solution
\(g(f(1))=g(7)=7\)
\(f(g(2))=f(9)=6\)
Question
Let functions \(f\) and \(g\) be defined by the graph below.
Evaluate the following:
\(g(f(5)) =\)
\(f(g(4)) =\)
Solution
\(g(f(5))=g(3)=1\)
\(f(g(4))=f(9)=8\)
Question
Let functions \(f\) and \(g\) be defined by the graph below.
Evaluate the following:
\(g(f(1)) =\)
\(f(g(3)) =\)
Solution
\(g(f(1))=g(9)=2\)
\(f(g(3))=f(9)=7\)
Question
Let functions \(f\) and \(g\) be defined by the graph below.